Question

△jkl and △mno are shown below.
which statement is true?
△jkl is similar to △mno.
△jkl is not similar to △mno.
there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Identify equal angles

In $\triangle JKL$, $\angle J = 58^\circ$. In $\triangle MNO$, $\angle M = 58^\circ$, so $\angle J = \angle M$.

Step2: Analyze side-angle relationships

In $\triangle MNO$, the sides adjacent to $\angle M$ ($MN$ and $MO$) are marked as equal, meaning $\triangle MNO$ is isosceles with $\angle O = \angle N$. In $\triangle JKL$, there is no indication that the sides adjacent to $\angle J$ ($JK$ and $JL$) are equal. For similarity via SAS (Side-Angle-Side) similarity, the ratios of the sides around the equal angle must be equal, which we cannot confirm here.

Step3: Evaluate similarity conditions

We only know one pair of equal angles, and no information about the proportionality of sides. AA (Angle-Angle) similarity requires two pairs of equal angles, which we do not have. SAS similarity requires proportional sides around the equal angle, which we cannot verify.

Answer:

There is not enough information to determine whether the triangles are similar.